204
RICHARD PAYNE
-
V(II)
+ CIOs-
=
(VCIOa+)*
(6)
The activation enthalpy calculated for this process by means of a nonlinear least-sauare techniaue was found to be 9.9 f 0.6 kcal./mole; and the entropy of activation was found to be -23 2 e.u. These
*
values are close to the values obtained for the correspondmg chromium(I1)-chlorate r e a ~ t i o n ,where ~ AH = 11.0 kcal./mole and Aij' = -22 e.u.
Acknowledgments. This research was supported in part by a grant from the Office of Saline Water.
Structure of the Electrical Double Layer at a Mercury Electrode in
the Presence of Adsorbed Perchlorate Ions
by Richard Payne Air Force Cambridge Research Laboratories, L. G. Hanswm Field, Bedford, Massachusetts (Received July 90,1966)
The specific adsorption of perchlorate ions on a mercury electrode from mixed solutions of ammonium perchlorate and ammonium fluoride has been studied by measuring the capacity of the double layer as a function of the composition of the solution at 25'. The adsorption closely resembles that of the nitrate ion reported previous1y.l The amounts adsorbed are calculated, and the capacity is resolved into its component parts with the aid of Muse-layer theory. From the analysis of the inner layer capacity, the standard free energy of adsorption is shown to be a quadratic function of the electrode charge: the constants of this function are evaluated and compared with the values calculated from surface pressure data. The component of the inner layer capacity measured at constant amount adsorbed depends on the amount adsorbed, and the capacity measured at constant charge is a function of the charge. The origin of the capacity hump occurring close to the electrocapillary maximum is discussed in terms of the components of the capacity. The unusual properties of this system are tentatively attributed to competitive adsorption of the solvent, but the possibility of specific adsorption of fluoride ions is also considered.
havior of the nitrate anion first noticed by Grahame and Soderberg2 primarily due to the quadratic charge dependence of the standard free energy of adsorpThe Journal of Physieal Chemtktry
(1)R. Payne, J , Phys. them., 69, 4113 (1985). (2) D. C. Grahame and B. Soderberg, J . C h m . Phys., 22, 449 (19~).
STRUCTURE OF ELECTRICAL DOUBLE LAYERAT
AN
205
Hg ELECTRODE
inner region of the double l a ~ e r . ~The ? ~ perchlorate ion closely resembles the nitrate ion in its electrocapillary properties3 although the geometrical structure which appears to be an important factor in the nitrate adsorption is quite different in the two cases. It is therefore of some interest to determine the extent to which the conclusions drawn from the study of nitrate ion adsorption can be applied to the adsorption of perchlorate ions. As before, it was decided to work with mixed solutions of the ammonium salt with ammonium fluoride at constant ionic strength. This considerably reduces the uncertainty due to the diffuse layer correction which, as noted previously, is inherently inaccurate where the anion is only weakly specifically adsorbed.
Experimental Section The capacity of the double layer at a droppingmercury electrode was measured for eight solutions of 2 M NKC10, (1 - x) M N H Z in water for 0 \< x 6 1 at 25' using the a.c. bridge described previously.6 The procedure was the same as that described in a previous paper.6 Potentials of zero charge were measured for all solutions by the method of the streamingmercury electrode' and were used subsequently to check the reproducibility of the reference electrode and liquid junction potential. The reference electrode used in all of 6he measurements was a calomel electrode in 1M KCI. Solutions were prepared volumetrically from permanganate-distilled water and A.R. grade salts. NH4C104was recrystallized from purified water, but NH4F was used without further pur%cation. As before, no evidence of impurities in the solutions was observed during the measurements.8 Mercury was purified by treatment with nitric acid followed by triple distillation in vacuo. Capillaries were prepared as described previously.6 All measurements were made in a water thermostat controlled to =kOo.05O.
35
+
Results The capacity is shown as a function of potential in Figure 1for eight solutions of x M NKC104 (1 - S) M NH4F at 25'. As in the case of nitrate, the characteristic hump on the anodic side of the electrocapillary maximum (e.c.m.) is developed primarily by the decrease in capacity on the far anodic end of the curve. The increase of capacity on the cathodic side of the hump is not so marked as in the case of nitrate. The perchlorate ion is evidently desorbed at potentials more negative than -1.2 v. in view of the apparent coincidence of the capacity curves in this region although the curve for l M NE4C10, a p p m to lie above
+
15
- 0:5
0
- 1.0
-1.5
~~
POTENTIAL V S N C A L ( V O L T ) Figure 1. Differential capacity of the electrical double layer in contact with solutions of x M NH'ClOa (1 z) M N H Z in water at 25": z = (1)0; (2) 0.0025; (3) 0.005; (4) 0.01; (5) 0.02; (6) 0.05; (7) 0.1; (8) 0.2; (9) 1.0.
+ -
the others even at extreme negative potentials. The results for this solution were not used in the analysis of the data. The capacit>iesand potentials at the e.c.m. are summarized in Table I. The capacity was integrated as before to give the function E+ = y' qE+ where y' is the interfacial tension relative to that of the 1 M NH4F solution at
+
(3) D. C. Grahame, Chem. Rev.,41,441 (1947). (4) D. C. Grahame, J . Am. Chem. SOC.,80,4201 (1968). (6) G. J. Hills and R. Payne, Trans. Faraday SOC.,61, 316 (1965). (6) R. Payne, J. Electroanul. Chem., 7, 343 (1964); Thesis, London, 1962. (7) D. C. Grahame, E. M. C o f i , J. T. Cummings, and M. A. Poth, J . Am. C h .Soc., 74, 1207 (1962). (8) Since NHdF is the salt of a weak acid (PICB = 3.17) and a week base (pKb = 4.76), the possibility of adsorption of neutral HF or NHs arises. A simple calculation shows that the product [HF] [NHs] will be -10-8 mole2 1.-2 in 1 M NHdF so that the concentrations of H F and NHs will be of the order of 10-8 mole/l. However, addition of HF and NHs to NHLF solutions has little effect on the capacity except at the far anodic end where the situation may be complicated by hydroxyl ion adsorption and discharge.6 Furthermore, the capacity-potential curve for 1 M NHLF closely resembles the corresponding curves for NaF and KF. It therefore seems reasonable to assume that neutral HF and NHa are not strongly adsorbed and do not appreciably affect the measurements.
Volume 70, Number 1 January 1966
RICHARD PAY"
206
Table I : Potential and Capacity of the Electrocapillary Maximum for Solutions of z M NEC104 (1 2) M',NH4Fin Water a t 25"
+
-
474.0 474.2 475 * 5 477.2
0.0 0.0025 0.005 0.01 0.02 0.05 0.1 0.2
472.7 473.9 476.7 480.1 488.6 500.1 512.9
489.0 498.4 513.5
IO
/:.
8
26.13 26.23 26.38 26.66 27.12 27.98 28.75 29.34
x = op
/'
6
' Emeaadw&s measured directly by the streaming-mercury Eeald was calculated by back-integration electrode method.' of the capacity-potential curve from the far cathodic end &ssuming a value for p of -20 pcoulombs/cm.z a t E = -1.5215 v. obtained from the data for 1 M N W , common to all solutions.
the e.c.m., q is the charge on the metal, and E+ is the potential measured with respect to a hypothetical cation reversible electrode. Since only diflerences of potential are required in the analysis and the concentration of cations remained constant, E + could be replaced by the measured potential EN~.I.The constants of integration were again evaluated by assuming equality of the capacity, charge, and interfacial tensions for all solutions at suEciently negative values of Q (-20 pcoulombs/cm.2). A partial check of the accuracy of t8hisprocedure was possible by comparison of the e.c.m. potentials calculated by the above (backintegration) method with the directly measured values. The agreement was usually better than 1 mv. although deviations of up to 1.6 mv. occurred in two cases. This was not so good as the agreement found for tho nitrate system but was considered satisfactory. The charge due to spec5cally adsorbed perchlorate ions (a') was calculated by graphical differentiation of the plots of the surface pressure @ with respect to chemical potential of the nitrate ions in solution according to the equationeJo -d@
=
RT/Fq' d In x
- E+dq
(1)
@ is defined by @ =
tf
-
&I+
(2)
where to+refers to the 1M N E F solution. q1is shown as a function of the charge on the metal and the concentration of N&CIOI in Figure 2. AS in the case of the nitrate ion and unlike those of iodide4and chloride,ll the curves diverge widely. The weak adsorption of
SURFACE CHARGE DENSITY q ( p C O U L / C M 2 ) Figure 2. Charge due to specifically adsorbed perchlorate ions (p') as a function of the surface charge density p and the bulk concentration of perchlorate.
the perchlorate ion is illustrated by the low maximum values of q1 attained (4pcoulombs/cm.2). Because of the small range of surface p m u r e s found in the experimentally accessible region, no attempt was made to fit the data to a theoretical isotherm. Instead, the values of p1 obtained by the graphical differentirtr tion method were used directly to calculate the charge due to diffuselayer ions (qd) by difference pd = - q -
Q'
(3) With the aid of the qd values and diffuse layer theory, the capacity of the diffuse double layer (Cd) and the potential difference across the diffuse layer (&) were calculated. The potential difference ( c $ ~ - ~generated ) acrom the inner region of the double layer by the specifically adsorbed charge was calculated by subtracting the potential of the e.c.m. in the absence of specific ad(9) E. Dutkiewicz and R. Parsons,J. Electroad. C h . , in press. (10) In the derivation of (1) it i s aasumed that the activity coefficient of the perchlorate ion is independent of the composition and
also that ammonium and fluoride ions are not specifically adsorbed. (11) D. C. Grahame and R. Parsons, J . Am. Chm. SOC.,83, 1291 (1961).
STRUCTURE OF ELECTRICAL DOUBLE LAYERAT BN Hg ELHIOTBODE
207
reaolved into its components as before by means of the identity12
l/,d + 1/,1C'bq'/dp
1/c' =
(5)
where
-
l/,@ = (bf#F-2/bp)pl
50
(6)
and
>
l/,Ic'
Y
= (b4m-2/bql),
(7)
N
i
8
E W
>-
a
-J
E
w
z .0.3 z m
8-
.-.-.-.
.-
'
03 0 E
IO
*-
$'
0 Q
d a:
The component capacity ,c' which is the capacity of the inner region measured at constant amount adsorbed has been referred to12 as the "base solution" capacity by analogy with the adsorption of neutral molecules from a base solution of constant salt concentration. Although this terminology is quite satisfactory in discussionsof specsc adsorption of anions like iodide and chloride where ,C' is approximately independent of the amount adsorbed, it is misleading in system is strongly dependent on like the present one where the amount adsorbed, and it will therefore not be used in the following discussion. The component of capacity measured at constant charge on the metal ,IC will be referred to as the adsorption capacity as before. As in all previously studied systems, g1c' can be replaced by the correspondin view of the linearity of ing integral capacity gg the plots in Figure 3. The nature of the adsorption process was investigated by consideration of the change of the inner layer capacity brought about by the adsorption process using the methods developed by Parsons.16J6 In Figure 4 the change of the inner layer capacity in the form -Al/c is plotted against q for seven concentrations of NH.,C104. Al/Ci is equal to 1/@ l/Gi where C: is the inner layer capacity for the 1 M NHZ solution in the absence of perchlorate ions. The form of the variation of -Al/@ with p is closely similar to that found previously for the nitrate system and again is characteristic of an adsorption isotherm in which the standard free energy of adsorption is a quadratic function of the electrical variable, ie., the charge q.16 Following Parsons, we write this quadratic dependence aa
0
3
4
6
8
SPEC. ADS. CHARGE q l ( ~ C O U L . / C M ~ Figure 3. Potential difference across the inner region of the double layer ( bm - a) as a function of the charge due t o specifically adsorbed perchlorate ions ( q l ) and the charge on the metal (q).
sorption (-0.474 v. os. N cal.), and the m u s e layer potential difference (42) was calculated from the mea& ured potential. 4m-2 is shown as a function of q1 for integral values of q in Figure 3. As was found for the nitrate system, tpm-2 is linearly dependent on ql, the slope declines as q increases, passes through 5ero a t q = 10 pcoUlombs/cm.2, and reverses sign at more positive values of p. This behavior is characteristic of an adsorption process in which the standard free energy of adsorption is a quadratic function of the electrode charge, which is usually observed in the adsorption of neutral organic molecules but not previously for inorganic ions, for which an approximately linear relationship is usually found.lJ1-14 The capacity of the inner region of the double layer (c')was calculated from the equation'* 1/c = 1 / c
+ 1/cd (1 + :?(4)
Values of bql/bq were obtained from plots of q1 v8. q (Figure 2) by graphical differentiation. c' was then
In B
=
In LL"
- (b/2)62
(8)
(12) R. Parsons, Tram. Faraday ~ o c . ,55, 999 (1969). (la) J. M.Parry and R. Pareons, ibid., 59,241 (1963). (14)R. Payne, J. C h . Phya., 42, 3371 (1966). (16) R. Parsons, J. h'ledroad. chem.,5, 3-97 (1963). (16) R.Parsons, ibid., 7, 136 (1964).
Volume 70,Number 1 January 1966
RICHARD PAYNE
208
b6p2/2 =
-10
5
- In [(b6p2f 3)/(b6pz
- 3)I
(11) where 8, is the value of 6 corresponding to the maximum in -Al/@ in Figure 4. Equation 11 is the analog of eq. 4.10 of ref. 15 derived for a Langmuir adsorption in which the standard free energy of adsorption is a quadratic function of the electrode potential rather than the charge. As noted by Parsons is linearly related to In x at concentrations sficiently high so that the last term in (11) can be neglected. Furthermore, (b/2)a2 is assymptotic to the value 3 at low concentrations, a result which does not depend on the form of the isotherm providing the system behaves ideally at low concentrations. The results of such a plot are shown in Figure 6. Although the concentration range is insufEcient to show the linear segment of (ll), the curve appears to approach the limiting slope corresponding to the value of b = 0.042 pcoulomb-2 cm.a previously calculated. The -ptotic value of 6,2 is approximately 60 pcoulombs2cm.-4 which leads to a value of
-5
1
+ In
0
IO
-10
SURFACE CHARGE DENSITY q (FCOUL./CM') Figure 4. Change of the inner layer capacity resulting from specific adsorption of perchlorate ions: z = (1)0.0025; (2) 0.005; (3) 0.01; (4) 0.02; (5) 0.05; (6) 0.1; (7) 0.2.
where In ,# is related to the standard free energy of adsorption by
In p
-AG"/RT (9) pmar is the maximum value of ,6 which occurs at a value of the charge qma, and 6 = Q - q m a . The change of the inner layer capacity is then given by the expression l/Ci
- l/Coi
=
=
RT/F{ [bq'
- (b6)z]dq1/dIn p ]
(10) -Al/C' is shown plotted against q1 for several values of q in Figure 5. As expected, the slope decreases with increasing q owing to the second term in the braces in (10) reaching a minimum value at q = 10 pcoulombs/cm.2. This corresponds to 6 = 0 since, according to Figure 4, the value of qmsx, Le., the charge at which the lowering of -l/C is greatest is approximately equal to 10 pcoulombs/cm.2. According to (lo), therefore, the slope of the plot for p = 10 pcoulombs/cni.2 in Figure 5 should be equal to RTb/F, from which b = 0.042 pcoulomb-2 cm.4. The value of b can also be estimated from the equation
IO
-I0 0
2
4
0
6
SPEC. ADS. CHARGE q ' ( p C O U L . / C M
1
Figure 5. Change of the inner layer capacity resulting from specific adsorption of perchlorate ions, as a function of the specifically adsorbed charge (4') and the charge on the metal (p).
STRUCTURE OF ELECTRICAL DOUBLE LAYER AT AN Hg ELECTRODE
I'
/'
200
P / a ,/.0
100 -0
>13// ,' I
3
-2
0
-I
LOG x Figure 6. Plot of eq. 11. 6, = qp - qmar where qp and qmsr refer to the value of the electrode charge corresponding to the maximum and minimum values of - Al/Ci, respectively, for a given concentration in Figure 4. The broken line corresponds to a value of b = 0.042 pcoulomb-z ~ m . ~ .
0
c5
0
5
from capacity data
IO
SURFACE CHARGE DENSITY q (~COULICM'
15
1
I
)
Figure 7 . Comparison of the charge dependence of the standard free energy of adsorption calculated from the surface pressure data with that calculated from (8) using a value of qmaX = 10 pcoulombs/cm.2 and b = 0.042 cm.'/pcoulomba.
b = 0.043 pcoulomb-2 cm.' in excellent agreement with the previously calculated values. The value of b obtained directly from the capacity data may be compared with that obtained from the surface pressure data by superimposing the surface pressure curves for different values of Q. The resulk of this procedure are compared with the corresponding variation of In p calculated from (8) for b = 0.042 p coulomb-2 cm.4 and qm.= = 10 pcoulombs cm.-2 in Figure 7. The two methods of calculation disagree
209
in two respects. Firstly, the maximum in In p clearly predicted by the well-defined capacity minimum in Figure 4 is not shown by the surface pressure data, and, secondly, the curve8 diverge at low values of q. The agreement is much improved by substituting b = 0.033 pcoulomb-2 ~111.~ in (8). However, the surface pressure data show systematic deviations from a common curve suggesting that the isotherm constants may be dependent on the charge and the method may therefore be unsatisfactory, although the absolute deviations are no more than 0.3 dyne/cm. and are possibly within the experimental error. The range of surface pressures found (7 dynes/cm.) was too small to allow fitting of the data to an isotherm by this method. The ratio of the maximum to the minimum values of -A l / c ' for a given concentration in Figure 4 should approach the limiting value -2e-"' or -0.446 at low coverages where the adsorbate theoretically obeys a Henry's law isotherm. The value of this ratio in the present situation varies in the range -0.18 to -0.49 for the concentration range 0.01-0.2 M . The low concentration value, therefore, is considerably higher than the theoretical value, suggesting either that the square-law dependence of In P on p is no longer valid at negative values of p where the peak occurs, as found in the case of nitrate adsorption, or alternatively that the isotherm constants are varying with the charge. Similar deviations from theoretical behavior noted in the adsorption of amyl alcohol have been attributed to the use of nonzero frequency capacities.16 However, this could not be the case in the present system, which suggests that the observed discrepancies may be due to other factors common to both systems.
Discussion I . Nature of the Capacity Hump. The total differential capacity (C) the capacity of the inner region (c')and the component of c' measured at constant amount adsorbed (,C)calculated from (4) and (5) are compared for several concentrations of NH4C104 in Figure 8. As in the case of nitrate solutions, the shape of the capacity curve is dominated by the dependence of $ on the concentration of N&C10,, i.e., the amount of adsorbed clod- ion, especially at the more positive charges. This is due as before to the approach of ,I@ to zero in (5) as q becomes more positive. At intermediate values of q, however, the adsorption term in ( 5 ) exerts an appreciable effect on the inner layer capacity which is readily apparent from a comparison of the curves in Figure 8b and c. The diffuse layer capacity also contributes noticeably to the development of the capacity hump (Figure 8a and b). Volume 70,Number 1 January 1966
RICHARD PAYNE
210
(C 1
I
x=o 0~01
.32
0.05 0.2
30 ,28
,26 12
8
4
0
\. \’
\-4
SURFACE CHARGE DENSITY q ( ~ C O U L Y C M ~ ) Figure 8. Components of the double layer capacity: (a) total capacity ( G ) ; ( b ) capacity of the inner region (CY); (c) capacity of the inner region measured a t constant amount adsorbed (*Ci).
As was stressed previously, this behavior is quite different from that observed in the adsorption of anions like iodide and chloride in which the shape of the capacity vs. potential (or charge) curve is dominated by the adsorption term in the positive region of polarization while the capacity measured at constant amount adsorbed is independent of the amount adsorbed within the experimental error. The difference in behavior between systems like nitrate and perchlorate, on the one hand, and iodide and chloride, on the other, is due not primarily to differences in the nature of the adsorption isotherm so much as to the form of the variation of the standard free energy of adsorption with the electrode charge, which is quadratic in the first group and linear in the second. It was suggested previously1 that the square-law dependence of In /3 on p characterized by the curves in Figure 4 was the result of the competing adsorption of solvent dipoles in the region of high field strength.l’ This interpretation implies either that the contribution, to the adsorption energy, of the coulombic interaction of the ionic charge with the metal is small as it would be, for example, if the center of charge were far The Journal of Physical Chemistry
removed from the electrode surface because of the large size of the ion or that the coulombic metal-ion interaction is swamped by the dipolefield interaction energy required to displace the solvent dipoles from the inner region in the adsorption process. In the case of nitrate, it was shown that the adsorbed ion occupied an anomalously large area on the electrode suggesting that several water dipoles might be replaced by the adsorption of a single ion, with a consequent decrease in the adsorption energy for the ion. Measurements of the surface excess entropy for the mercury-aqueous NaN03 system18 are also consistent with the release of large amounts of bound water in the anodic region of polarization. Although the Clod- ion is tetrahedral in contrast to the planar there is no reason t o geometry of the nitrate believe that a similar process cannot occur in the perchlorate adsorption, and indeed the close similarity of the electrocapillary behavior of the two systems strongly suggests that this is the case. An alternative possibility that was discounted in the previous paper is that the competing species is not the solvent but the F- ion. Although there is considerable experimental evidence, mainly from the work of Grahamel3tz0 that fluoride is not specifically adsorbed, it should be pointed out that this conclusion relies heavily on Gouy-Chapman diffuse layer theory under conditions where, as is well known,21 the calculation is critically sensitive to the experimental data. Thus, Grahame’s data for 0.1 N KFZ2suggest that fluoride might be specifically adsorbed by amounts of up to -3 pcoulombs/cm.2 at this concentration. The uncertainty in the calculation can be judged from the fact that he regarded this value as zero within the experimental error.2 Bockris, Devanathan, and Mullerz3 have given a value of 9.5 pcoulombs/cm.2for specifically adsorbed fluoride ion at p = 10 pcoulombs/cm.2 without, however, specifying the solution concentration. Although this value is probably too large owing to the (17) The squardaw dependence arises not from the increasing distortional polarization of the adsorbed solvent molecules but from the squeezing out of the weakly adsorbed ions by the solvent, probably aided by a specific interaction of the negative end of the water dipole with the metal and also the large size of the ion. This results in a decrease in the effective length of the dipole formed by the ion and its image in the outer Helmholtz plane and, hence, in the energy of interaction of this dipole with the field. (18) G. J. Hills and R. Payne, Tram. Faraday SOC.,61, 326 (1966). (19) L. Pauling, “The Nature of the Chemical Bond,” Cornel1 University Press, Ithaca, N. Y.,1948. (20) D.C. Grahame, J . Am. Chem. Soc., 76, 4819 (1964); 79, 2093 (1967). (21) E.M. Joshi and R. Parsons, Electrochim. Acta, 4, 129 (1961). (22) D.C. Grahame, unpublished data. (23) J. O’M. Bockris, M. A. V. Devanathan, and K. MWer, Proc. Roy. SOC.(London), A274, 66 (1963).
STRUCTURE OF ELECTRICAL DOUBLE LAYER AT AN Hg ELECTRODE
dubious theory24on which it is based, it is nevertheless probable that the result is qualitatively correct and that the fluoride ion merely differs in degree from the other halide anions.26 In that case, it is to be expected that the effect of specific adsorption of fluoride ions will be felt in a system like the present one in which the anion being studied is itself only weakly adsorbed. It should be pointed out also that, if fluoride is in fact specifically adsorbed, the use of eq. 1, which was derived on the assumption that fluoride ions are present only in the diffuse layer, will be incorrect although the errors introduced into the calculations from this source are likely to be small. In view of the facts that the formation of the capacity hump in nitrate and perchlorate solutions is primarily due to the effect of the anion adsorption on the capacity measured at constant amount adsorbed and that the shape of the capacity vs. charge curves is closely similar to that of the pure fluoride solution, it seems unreasonable to suppose that the hump in the latter case is due to a maximum in the orientational contribution to the dielectric constant of the solvent layer as is widely accepted.26 A more natural explanation is found in terms of the interplay of ion and solvent adsorption in this region of polarization, especially in view of the mounting e v i d e ~ i c e28~ that ~ ~ ~ the ' ~ preferred orientation of the water molecule on mercury is that with the negative end of the dipole facing the metal. 2. Potential Difference Generated by Speca$cably Adsorbed Anions. The potential difference (V"'+) generated across the inner region of the double layer by specifically adsorbed perchlorate ions is plotted against the charge due to the adsorbed anions for several constant values of p in Figure 3. The results closely resemble those for nitrate adsorption in which the slope of the linear plots decreases with increasing q, passing through zero at q = 10 pcoulombs/cm.2, and actually reversing sign at the most positive value of q. This behavior is to be expected since the slope is related to the functional dependence of In p on q which evidently possesses a maximum value around q = 10 pcoulombs/cm. 2, The reciprocal scope (dql/br$m-z)Q of the lines in Figure 3 has the dimensions of capacity denoted in ( 5 ) is indeby qlCi. As in all systems studied so far, pendent of the amount adsorbed (in view of the linearity of the plots in Figure 3) and can therefore be replaced by the corresponding integral capacity &'. According to Figure 3, therefore, the capacity measured at constant charge on the electrode increases to an infinite value at p = 10 pcoulombs/cm.2 and assumes a negative value for p > 10 pcoulombs/cm.2. Although it is possible to interpret the dependence
211
of ,IKi on Q in terms of variation of the position of the inner Helmholtz plane (I.H.P.) with q, it seems much more realistic to abandon the Grahame-Stern model of the inner layer in this kind of system. Although Stern's theory29of specific adsorption and, in fact, any treatment invoking an equation of state for the adsorbed ions based on the Langmuir isotherm take into account the replacement of solvent molecules in the adsorption process as was recently shown by Frumkin,m the permanent dipole of the solvent molecule is nevertheless not accounted for.a1-a3 It appears that the solvent layer could generate a large potential difference under certain conditions,l so that modifications in the structure of the layer due to the adsorption process will contribute to +m-2 and should be taken into account. The zero and negative slopes of -c$"-~ us. p1 would result from the replacement of strongly negatively oriented solvent dipoles by the ion. A similar result would be expected in a mixed-ion adsorption process of the kind that might occur here if fluoride ions were also specifically adsorbed. The form of the variation of $m-2 for the replacement of one anion by another of approximately equal (lateral) size will presumably (24) M.A. V. Devanathan, Tram. Faraduy Soo., 50, 373 (1954). (25) The success of Devanathan's theory in accounting for specSc adsorption of inorganic ions is due to the fortuitous approximate constancy of the component integral capacities K,-1 and KI-Z
(Devanathan's notation) in the systems considered (potassium halides). It is eaaily shown that K1-z and the series combination of K,-I and KI-2 should be replaced by the partial derivatives (bql/bp-z)p and (bq/b4m-*)pl, respectively, ;.e., the components ,IC' and *Ciof the differentialinner layer capacity which, as Grahame' and Parsons'' have shown, is almost independent of q1 and not strongly dependent on q in the anodic region of polarization for these systems. These properties were quite unexpected and, aa the present system suggests, are unlikely to be of general occurrence since both the dielectric constant and the thickness of the inner region are expected to depend strongly on the amount of adsorption. The calculation of q1 for fluoride ion adsorption from electrocapillary and capacity data using the thermodynamic method and m u s e layer theory, with the reasonable assumption that cations are not speci6caUy adsorbed when q is positive, can be assigned reliable limits of error. No such limits can be assigned to Devanathan's method of calculation since nothing is known about the charge and concentration dependence of K-1 and K1-z in this system nor is the method of calculating these parameters of proved reliability. (26)R. Parsons, Aduan. Electrochem. Electrochem. Eng., 1, 1 (1961). (27)A. N.Frumkin, 2.A. Jofa, and M. A. Gerovich, Zh. Fiz. Khim., 30, 1455 (1956). (28) E. Blomgren, J. O'M. Bockris, and C. Jesch, J . Phys. Chem., 65, 2000 (1961). (29) 0. Stern, 2.Elektroch., 30, 508 (1924). (30) A. N.Frumkin, J . EZectroad. Chem., 7, 152 (1964). (31)The permanent dipoles of the adsorbing species and the replaced solvent molecules were considered by both Frumkinsz and Butler@to explain the shift of the e.c.m. potential accompanying the adsorption of organic molecules. Similar arguments can, however, also be applied to the shift of the potential at (constant) values of the charge other than q = 0. (32)A. N. Frumkin and B. B. Damaskin, "Modern Aspects of Electrochemistry," No. 3, Butterworth and Go. Ltd., London, 1964, p. 149. (33) J. A. V. Butler, Proc. Roy. SOC.(London), A122, 399 (1929).
Volume 70,Number 1 January 1966
RICHARD PAYNE
2 12
adsorbed at constant charge in Figure 9. As in the case of nitrate, the points fall on a common curve for q > 2 pcoulombs/cm.2 (because of the small dependence of pKi on q at constant q1 in this region). The linear relationship found for nitrate is probably fortuitous. Although the interpretation of ptKiin terms of a parallel-plate condenser model depends on the assumption that the simple GrahameStern picture of the double layer is correct, no such restriction applies to the discussion of the capacity measured at constant amount adsorbed (qKi)which can still be regarded as the capacity of the condenser formed by the metal and the outer Helmholtz plane irrespective of the nature of the adsorption process. However, the interpretation of the dielectric constant (ei) and thickness (x2) will depend on the model of the adsorbed state. Thus, in the case of nitrate adsorption, pKiwhich is given by
32
X
X
,Ki=
V
P
-2 I2
24 J
2
4
6
8
I
I
I
I
SPEC. ADS CHARGE q' ( y C O U i . / C M
)
Figure 9. Integral capacity of the inner region of the double layer measured a t constant amount adsorbed (,Ki)as a function of the specifically adsorbed charge (q') and the charge on the metal (q). Values of q indicated below each symbol are in microcoulombs per square centimeter.
depend on the closeness of approach of the ion to the metal and could be zero or positive. It seem significant that all studiw of ion adsorption from solutions of a single salt4J1J8J4 give approximately parallel plots of @'"2 us. q' even for anions aa large aa the benzenedisulfonate ion, which would be expected to eliminate large numbers of water molecule4 from the inner layer. This fact suggests that the supposedly inert fluoride ion and not the solvent is the competing species in the present system. Although it is unlikely that this question can be answered conclusively by thermodynamic measurements of the type described here, it is probable that considerable insight into the problem can be gained by a systematic study of ionic adsorption from mixed-electrolyte solutions. 3. T h e Capacity of the Inner Region at Constant Amount Adsorbed. The strong dependence of the component of the inner layer capacity measured at constant amount adsorbed (,Ci) on the perchlorate concentration in the solution and hence on the amount adsorbed is illustrated in Figure 8. The corresponding integral capacity (@Ki)is plotted against the amount The Journal of Physical Chemistry
ei/4rx2
(12)
was regarded as the capacity of the inner region consisting of only solvent molecules and nitrate ions, i.e., no adsorbed fluoride ions. The decrease of ,Ki with q1 was interpreted as primarily a decrease in ei resulting from displacement of the solvent dielectric. In view of the magnitude of the effect, this still seems the most likely interpretation for both systems. However, if fluoride were specifically adsorbed at the more positive charges and replacement of these ions were responsible for the observed variation of cpm-2 with q1 in this region, the decrease of qKi with q1 observed would have to be attributed to increase of the thickness since the dielectric constant would presumably be little aiYectedea4 In view of the large size of the perchlorate ion, it is not unreasonable to suppose that the average thickness of the inner layer would increase with the amount adsorbed if fluoride ions were being replaced, so that both interpretations are qualitatively acceptable. The answer to this problem also must await a more systematic study of mixed-ionic adsorption. Acknowkdgmenk. The author wishes to acknowledge the use of laboratory and computer facilities at the University of Bristol, England, where the experimental part of this work was performed. The support of the Department of Scientific and Industrial Research (British Government) in the form of an apparatus grant and a Senior Research Fellowship, during the tenure of which this work was done, is also gratefully acknowledged. (34)It is assumed in this discussion that the values of 91 are not sufficiently in error owing to incorrect w e of eq. 1 to invalidate the whole analysis.
